Quivers, curves, Kac polynomials and the number of stable Higgs bundles
Introductory Workshop: Geometric Representation Theory September 02, 2014  September 05, 2014
Location: SLMath: Eisenbud Auditorium
14075
In the early 80's Kac proved that the number of indecomposable representations
of a given quiver (and a given dimension) over a finite field is a polynomial in the size of the finite field.
Hua later gave an explicit formula for these polynomials and subsequent representationtheoretic or
geometric interpretations for these polynomials were given by CrawleyBoevey, Van den Bergh, Hausel
and others, leading to a beautiful and still mysterious picture.
The aim of this minicourse is to explain a 'global' analog of some of these results, in which the category
of representations of a quiver gets replaced by the category of coherent sheaves on a smooth projective curve.
As an application, we will give a formula for the number of stable Higgs bundles over such a curve defined
over a finite field.
Schiffmann Notes

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